You could try the porta-grazer, OR try a hay net but put it up high enough, so no risk of it getting caught. I understand there are risks with hay nets, but I've always put mine high up enough.
If the BO is upset about you giving your horse extra hay (even though it's not 'extra', it's NECESSARY, she should be providing this) then maybe she needs to up her prices & she needs to understand that horses need forage.
For example. My old BO was cheap, & didn't believe in horses needing forage 24/7. Yet charged over $450 for board. EXPENSIVE!
Plenty of horses there developed ulcers. She would put them on a 12 on, 12 off schedule. That's how my horse developed ulcers.
I moved her to a new place, now she has forage 24/7 & is also outside 24/7. She hates stalls, but I know everyone is different. I prefer my horse to be out.
I am also paying less for board, & getting better care. So it really just depends.
It's basic care, period. I wouldn't feel comfortable if my horse had an empty stomach all night long. They need constant forage. It's not worth the risk of ulcers/colic. Trust me.
I'd move my horse if this continues, better to be safe than sorry. The price may seem great, but the care is not. Up to you, but 24/7 turnout & forage sounds like a better deal.